Science &Technology
Multiscale Modeling of Lipid Bilayer Interactions with Solid Substrates
David R. Heine, Aravind R. Rammohan, and Jitendra Balakrishnan
October 23rd, 2008
RPI High Performance Computing Conference
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Outline• Background
– structure of lipid bilayers– applications of supported lipid bilayers
• Modeling challenges• Atomistic modeling• Mesoscale modeling• Experimental work• Conclusions
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Lipids and Bilayers
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Technological Relevance of Supported Lipid Bilayers• SLBs are important for various biotech applications
– Biological research• Model systems to study the properties of cell membranes• Stable, immobilized base for research on membrane moieties• Biosensors for the activity of various biological species• Cell attachment surfaces
– Pharmaceutical research• Investigation of membrane receptor drug targets• Membrane microarrays: High throughput screening for drug
discovery– How does bilayer-substrate interaction affect bilayer behavior?
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Supported Lipid Bilayers at Corning• Applications: Membrane-protein
microarrays for pharmaceutical drug discovery
• Substrate texture is important in the adhesion and conformation of bilayers on the surface– Crucial for the biological
functionality of bilayers
• Objective: Quantify the effect of substrate topography and chemical composition on bilayer conformation and dynamics
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Bilayer Length & Time Scales• Bilayer dynamics vary over large length and time scales, suggesting a
multiscale approach.
Undulations:
4 Å – 0.25 mm
Bilayer Thickness: 4 nm
Area per lipid: 60 +/- 2 Å2
Stokes Radius: 2.4 nm
Length Scales
Peristaltic Modes:
1-10 ns
Undulatory Modes
0.1 ns – 0.1 ms
Lateral Diffusion
Time: 4 ps
Bond Vibrations: fs
Membrane Fusion: 1-10 s
Time Scales
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Multiscale Approach• Atomistic model
– capture local structure and short term dynamics• Mesoscale model
– capture longer length and time scales– sufficient to look at interaction with rough surfaces
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Atomistic Model• The bilayer is composed of 72 DPPC
lipid molecules described in full atomistic detail using the CHARMM potential
• Water uses the flexible SPC model to allow for bond angle variations near the substrate
• The substrate is the [100] face of -quartz with lateral dimensions of 49 x 49 Å described by the ClayFF potential
ji ij
ji
ji ij
ijo
ij
ijoijononbond r
qqerR
rR
DE0
26
,
12
,, 4
2
lipid
water
substrate
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Simulation Technique• System is periodic in x and y
directions with a repulsive wall above the water surface in the z direction
• NVT ensemble must be used since pressure control is prohibited by the solid substrate
• Temperature is maintained at 323K with a Nose-Hoover thermostat
• Total energy and force on the bilayer are extracted during the simulation.
Heine et al. Molecular Simulations, 2007, 33(4-5), pp.391-397. Substrate
Water
Bila
yer
Water
Lipids
Upper leaflet
Lower leaflet
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Simulation Technique• System is periodic in x and y
directions with a repulsive wall above the water surface in the z direction
• NVT ensemble must be used since pressure control is prohibited by the solid substrate
• Temperature is maintained at 323K with a Nose-Hoover thermostat
• Total energy and force on the bilayer are extracted during the simulation.
Heine et al. Molecular Simulations, 2007, 33(4-5), pp.391-397.
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Comparison with Experimental Measurements
SFA Measurements Between Substrate and Bilayer
Bilayer-Substrate Interaction Energy from Simulations
Simulations show an energy minimum at a separation of 3 to 3.5 nm
Experimental measurements show a repulsion starting around 4 nm and pullout at 3 nm separations
courtesy J. Israelachvili, UCSB
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Bilayer structure near the substrate
• Lower monolayer is compressed in the vicinity of substrate
• Upper monolayer seems relatively unaffected
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Effect of substrate on lateral lipid diffusion• Reduction in lateral
diffusivity observed, compared to free bilayers
– Bulk simulations match diffusivity of free bilayers
• Suppression of transverse fluctuations near substrate inhibit a key mechanism for lateral diffusion
Experimental valueFor free bilayers
Transverse lipid motion enables lateral diffusion
Substrate reduces transverse motion & reduces diffusivity
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Atomistic Simulation Results• MD simulations show bilayer-substrate equilibrium
separation of 3 – 3.5 nm, in agreement with SFA experiments
• Lateral diffusion of the lipid head groups decreases as the bilayer approaches the substrate
• Suppression of transverse fluctuations may be responsible for reduced lateral diffusion
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Mesoscopic Model
Membrane
Substrate
Continuum solvent
• Dissipative force– Formulation based on
Newtonian solvent viscosity
vaF ijwaterEDISSIPATIV
6
VECONSERVATIRANDOMEDISSIPATIV FFFdtvdm
ijwaterB
RANDOM
rTkDtttDF
6)'(23
• Random force– Formulation based on
fluctuation-dissipation theorem
• Conservative force– Elastic stretching of bilayer– Bending modes of bilayer– Surface interactions– Other (electrostatic, etc.)
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Mesoscopic Modeling of Supported Lipid Bilayers• Continuum representation
to study large length and time scales– 1 m2, 1 ms
• Allows study of bilayer behavior on textured substrates
• Dynamic model that includes effect of solvent and environment All dimensions in nanometers
z axis not to scale
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x
y
0 25 50 75 1000
25
50
75
100
z: 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12
x
y
0 25 50 75 1000
25
50
75
100
z: 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
Mesoscopic Model Results
Substrate topography contours Membrane topography contours
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Mesoscopic Model Results
Maximum and Minimum Separation
-10123456789
0 3 6 9 12 15Roughness in nm
Sepa
ratio
ns in
nm
Min_SepMax_SepMembrane
Coating Membrane spanning
MaximumSeparation
MinimumSeparation
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Mesoscopic Model Results• Allows study of bilayer on micron and microsecond scales
• Minimum surface roughness of 4-5 nm required for membrane spanning conformation
• Spanning configuration important for maintaining bilayer mobility
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AFM measurementsSpreading of Bilayer on Synthetic Substrates
AFM image & measurements
courtesy Sergiy Minko,
Clarkson University
Ref: Nanoletters, 2008, 8(3), 941-944
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AFM measurementsSmoothening of membrane on rough substrates
AFM image & measurements
courtesy Sergiy Minko,
Clarkson University
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Substrate roughness (nm)
Sep
arat
ion
from
subs
trate
(nm
)
0 2 4 6 8 10 12 14
0
2
4
6
8
10
Minimum SeparationMaximum Separation
Membrane conformation vs.substrate roughness
• Model shows membrane coating up to about 4-5 nm• AFM images show membrane coating 5 nm particles
Lipid membrane conformationNumerical and Experimental Results
AFM images courtesy Sergiy Minko, Clarkson U.Macroscopic model predictions
MaximumSeparation
MinimumSeparation
~ 5 nm
SUBSTRATE
BILAYER
Roiter et al. Nanoletters 8, 941 (2008)
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Conclusions• MD simulations show bilayer-substrate separation of 3 – 3.5 nm, in agreement
with SFA experiments
• MD simulations show reduced lateral diffusion in lipids as the bilayer approaches the substrate
• Mesoscopic model shows membranes coat particles up to 4 – 5 nm in diameter, in agreement with AFM observations
• Larger surface features are needed to achieve separation between bilayer and substrate
• High-performance computing has opened up new approaches for understanding biomolecule-substrate interactions, which aids design
• There is still plenty of room to grow as these models are still restricted in terms of size, timescale, and complexity
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Acknowledgements• Professor Sergiy Minko & his group at Clarkson U.
• Professor Jacob Israelachvili & his group at U. C. Santa Barbara
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Lipid Behavior on Nanoparticles• Bilayer conforms to
Nanoparticles < 1.2 nm
• Bilayer undergoes structural re-arrangement involving formation of holes between 1.2 – 22 nm
• Beyond 22 nm bilayer
envelops the particle
Ref: Nanoletters, 2008, 8(3), 941-944